My first reaction is that you should leave the probabilities as fractions. For A and B, your answers in post #6 are both close so you likely worked them correctly, but the exact answers are [MATH]P(A)=\frac 4 9[/MATH] and [MATH]P(B) = \frac{15}{16}[/MATH]. Your answers are decimal approximations and there is no need for that. Post #9 is correct if you use the fractional value.
To do [MATH]P(A \cap D)[/MATH] you need to respond to my post #3 for that region.